CROUCH AND KUPKE
Volume Change by Density. Ribonuclease in 0-8 M Guanidinium Chloride? T. H. Crouch$ and D. W. Kupke*
Av
+
ABSTRACT:Volume changes ( accompanying interactions of proteins with other substances are conveniently determined in quantity with the rapid density techniques now available. It is shown that by constructing only two density-composition tables over the concentration range of interest of a proteinperturbing substance, the volume changes of interest and the partial specific volumes (I;) for each component in a threecomponent system can be generated as a smooth function of perturbant concentration. The AV of mixing, the A V in transporting protein from one concentration of perturbant to any other, and the A V in transporting the perturbant from solvent to protein solution can be calculated. The experimental system, water-isoionic ribonuclease-guanidinium chloride, was studied by this approach with three different rapid densimeters (two magnetic designs and the vibrating tube type). A V values for transporting ribonuclease from water to guanidinium chloride solutions between 0 and 8 M were positive and exhibited an apparent transition region between about 2 and 4 M guanidinium chloride a t 20 “C. AVvalues for trans-
porting the guanidinium chloride from water to water ribonuclease were also positive but generally smaller; a marked reduction in these volume increases commenced a t a substantially lower concentration of guanidinium chloride ( 0.2); these increases in density could not be unambiguously ascribed to evaporation. Since the objective was to maintain a constant molality of protein throughout the density series as the molality of GdmCl (g3/gz) was varied, the appropriate volumes of a protein stock solution were added, via gas-tight syringes, to the dry GdmCI. The value of g3/gl,
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after correction for the difference i n air buoyancies of the weighed material. was calculated via: g3/g1 = g3/qAl
- WzO)
where W1° is the known weight fraction of RNase in the stock solution containing no GdmCl and m p is the buoyancy-corrected mass of this solution added to the corrected mass, g3, of the GdmCI. Densities were determined on triplicate samples at 20 O C with one of two different magnetic suspension densimeters (Senter. 1969: Almeida and Crouch, 1971)3 or by the electronic vibrating-tube method (Mettler/Paar, Model DMA 02C). On occasions. samples of the same solution were compared in the three instruments concurrently. These densimeters gave comparable results for the purpose at hand, although the magnetic method was about four times more rapid and required about one-third as much material. In general, theprecisions with replicate samples of a given solution were within 2 to 4 parts in IO6 in the density. The overall precision with separately prepared solutions of GdmCl with a given stock solution of RNase ranged from 5 to 10 parts in IO6. For the calibrations, water solutions of vacuum-dried sucrose ( U S . National Bureau of Standards, Lot 17) were used in conjunction with the density-composition tables a t 20 "C (Plato, 1900). Water solutions of heat-dried Suprapur grade cesium chloride (E. Merck, Darmstadt, Germany) were also prepared and used as secondary calibration standards for convenience in the higher density range where sucrose solutions become viscous. Results and Discussion Figure 1 shows the densities a t 20 "C of the water-GdmC1 mixtures (curve 1 ) and those of water-RNase-GdmC1 (curve 2) as a function of W3O,the weight fraction of GdmCl in water (exclusive of the protein in curve 2). Thus, for curve I , W3O = g3/(gl g3) = W3 at any composition, whereas in curve 2, W3" > W3owing to the presence of a constant amount of protein per gram of water. By this choice of units for the concentration
+
Details for the theory and practice of the magnetic method are described by Kupke and Beams (1972).
V O L U M E C H A N G E BY D E N S I T Y
TABLE I:
Coefficients of Eq 7 for Curves of Figure 1. Curve 1 (HzO-GdrnCI)
Curve 2 (HZO-RNase-GdrnCI)
0.998 265 3 f 3.15 X 0.296 306 4 f 5.10 X -0.129 821 5 & 1.50 X IO-' 0.725 210 8 f 1.77 x IO-] -2.593 957 f 1.05 6.683 422 f 3.42 -11.132 93 f 6.21 10.599 57 f 5.87 -4.328 860 f 2.26
1.013 362 7 f 1.02 X 0.288 422 9 f 5.71 X -0.142 976 4 f 8.89 X 0.668 828 0 f 5.45 x -1.598 501 1 f 1.57 X IO-' 1.997 452 8 f 2.13 x 10-I -0.984 268 5 f 1.10 X IO-1
Coeff of
w3
variable, the density difference between the two curves at any W3O is viewed at the same mass ratio of GdmCl to water. The data in curve 2 are from measurements using six different stock solutions of RNase in water which varied in weight fraction, W2O [=gz/(gl + g2)], from 0.048 to 0.062 on the basis of dry-weight analyses. The concentrations of these solutions were not adjusted to a common value to avoid evaporation and other error attending such meticulous manipulations. Hence, the points for curve 2 represent the data after normalizing all density values to those for a standard stock solution of weight fraction, WzO@)= 0.05 before any GdmCl was added. This reduction is justified because the values of $2 were found to be independent of RNase concentration within the error of the method at various levels of GdmCl over the range encompassed. The raw data for this normalization were treated as outlined in Appendix A. The data points (57 for curve 1 and 117 for curve 2, as normalized) are omitted from Figure 1; the smooth curves are computer-drawn representations based on polynomial regression analyses. Both curves fit the form: p =
N UjW3i i=O
(7)
where the coefficients, ai, of W3l are as listed in Table I. THe values of N (8 for curve 1 and 6 for curve 2) were chosen such that the variance was at the first minimum with respect to N . The standard error was f 1.22 X g/mL for the waterGdmCl series and f 2 . 6 4 X g/mL for the series containing RNase. With the densities known for any composition of a series, such as the 2 series in Figure 1, the total volume change, AV,,,i,, of mixing together assigned masses of any two solutions in a series can be calculated. Details for this procedure are outlined in Appendix B. If p is linear with c2 (curve 2), the method can be applied to any concentration of protein desired; hence, AVmixcan be calculated for a solution from curve 1 mixed with a solution from curve 2. These volume changes may be useful in constructing other experiments, but they are not dealt with further here. To illustrate the method of obtaining the volume change upon transporting protein from one concentration of perturbant to another, we may focus on two pairs of points on the two curves of Figure 1. Each pair of points is taken at a specified value of W3O. We choose the first pair where no GdmCl is present (W3O = 0) and the second pair at W3O = 0.50 (-6 M GdmCI). In principle, an amount (50 mg) of RNase is being transported from 1 g of water to another gram of water containing 1 g of GdmCl. Since the total weight fraction, W2, of RNase can be calculated for the two points in the upper curve (Appendix A), the values of 42 are given by eq 5 after multiplying W2 by the density in each case to obtain the respective
values of c2. Hence, the difference, A42, gives immediately the change in volume for carrying 1 g of RNase from water to 6 M GdmCl via eq 6; no other information is required. Obviously, this exercise may be repeated in order to obtain the volume change in transporting the protein component between any of the GdmCl concentrations encompassed in Figure 1. For this purpose, it is convenient to calculate the values of $2 at suitable intervals over the total range of W3O. Figure 2 shows $2 as a function of W3O (and the molarity of GdmCl in the protein solution). The points represent experimental values, while the smooth curve represents the values of $2 calculated from the two smoothed curves in Figure 1. The standard error of the data points with respect to the generated curve is f0.0008 mL/g. It is apparent that the specific volume of RNase is generally greater in GdmCl at all concentrations than in water, even after maximal denaturation of the protein in this salt (>4 M). This result may seem surprising in view of the standard explanation that the exposure to water of hydrophobic residues on the protein should cause a contraction in the specific volume. It should be recalled, however, that such volume changes depend on the differences in the various interactions of all components and cannot be predicted on the basis of a single kind of interaction between only the protein and the water. We have observed this increase in 42 for RNase at denaturing concentrations of GdmCl with a variety of RNase preparations over a period of several years. On the other hand, the addition of P-mercaptoethanol (0.005 to 0.1 M) gave rise to a precipitous drop in the values of $2 (>-0.013 mL/g) at GdmCl concentrations between about 3 and 6 M. Presumably, the random coil form interacts much more intimately with solvent than do the conformations with intact disulfide bridges. The concentration range from the crest to the center of the shallow well in Figure 2 (-1.9 to 4 M GdmCI) corresponds with the region defined by Hantgan et al. (1974) and others for the transition to a denatured conformation. (Note: a much deeper well was observed with some preparations which had stood several days after mixing; these values are not included in Figure 2.) The AVfor transporting 1 g of the denatured protein from 4 M GdmCl to higher concentrations of the salt increases rather remarkably (-+0.01 mL/g2 or -+137 mL/mol of RNase from 4 to 8 M GdmCl). A similar effect was noted also by Skerjanc et al. (1970) for chymotrypsinogen in high concentrations of urea. If the RNase is maximally denatured above 4 M GdmC1, the increase in volume upon transporting this protein from 4 M to higher concentrations of GdmCl might be explained by the loss of electrostricted water to the bulk solvent phase. RNase, however, could not be salted out in saturated GdmCl at 20 'C (W3O = 0.675). Copious precipiBIOCHEMISTRY, VOL. 1 6 , NO. 1 2 , 1 9 7 7
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w; F I G U R E 2: Apparent specific volume, $ 2 , of isoionic ribonuclease A vs. weight fraction, W3O, of guanidinium chloride with respect to water, and vs. the molarity, M3. of guanidinium chloride in the ribonuclease solutions (20 "C). The points represent the values of ~$2 calculated from the experimental values of the densities (-30 data points clustering at W,O 0 are omitted). The solid curve represents values of $12 calculated from the smoothed curves of Figure I .
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tation ensued upon reducing the temperature, but the supernate contained nearly all of the RNase. (Indeed, it appeared that the presence of 5% RNase reduced the solubility of GdmCl slightly, relative to the same value of g3/gl in water alone.) Since the values of LT and $ of a component are often composition dependent, the partial volumes of the nonprotein components should be taken into account (see below). We assume that the values of $ 2 in Figure 2 are equivalent to E2 a t each concentration of GdmCl since no dependence of $12 on c2 was apparent experimentally at selected values of W3. Combining the values of 52 and E3 for curve 2 of Figure 1 into the relation Z,U,c, = I , the values of E l are obtained by difference. Similarly, the values of El for curve 1 of Figure 1 (the protein-free series) are obtained after calculating E3 in that system. The values of E3 in each curve were calculated with eq 2 after determining the slopes via computer from the smoothed curves of Figure 1 in which the density values obtained by eq 7 with the coefficients of Table I were used to convert the weight fractions to ~ 3 Curves . ~ showing the variation of El in the presence and absence of RNase, respectively, as a function of GdmCl concentration are depicted in Figure 3a, and those for the variation of E 3 in the same two media are shown in Figure 3b. The differences between values of El and between values of E3 a t a common value of W3O resulting from the presence of RNase are seen to be too small to warrant confidence in them without further repetitive experiments. In other systems such differences may be more dramatic. Nonetheless, the trends suggest that E l decreases slightly and that E 3 increases slightly with W3O after RNase is presumably denatured maximally in this system beyond 4 M GdmCI. The apparent divergence between values of E3 as W3O 0, however, is dealt with presently because, if true, a substantial difference in the
-
It is often simpler in practice to eliminate c j for the calculation of C3 by rewriting eq 2 as follows:
-03 = P - ( 1 - W 3 ) ( d P / d W 3 ) m , T , P P2
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interactions of GdmCl in water and in water RNase is indicated a t very low concentrations of this salt. I n passing, the polynomial fittings to the curves of Figure 1 become insensitive as the concentration of GdmCl approaches zero; therefore, the curves of Figure 3b lead to an inaccurate representation of the values of E3 in the two solvents as W3O 0. The volume change on transporting the guanidine salt from water to water RNase is expressed as a function of W?Oin Figure 4. This volume change per gram of GdmCl is given by the difference in the apparent specific volumes, $3(r) - $3 = A43, of GdmCl in the two solvents a t any given mass ratio of GdmCl to water (where r refers to the RNase solutions). The value of $3 in each solvent (water and water RNase) at a particular value of Wj0 was calculated according to eq 5 via the densities from eq 7 and Table I and by applying the density of pure water (0.998234 g/mL at 20 "C) and that of the GdmC1-free protein solution (1.013363 g/mL at 20 "C) for the appropriate values of po. Unfortunately, these volume differences at the higher values of W3O approach the limits of the precision exercised in our experiments. The trend in 543 with W j 0 ,however, is essentially accurate, and the values of 143 are of the same degree of reliability as the two smoothed curves which were generated from the experimental values of the two density-composition tables. The curve in Figure 4 shows that the protein in 1 g of water titrates the guanidinium salt such that the volume increases more at any given value of W3O than when the same amount of this salt is added to 1 g of water alone. These volume differences are greater a t the denaturant concentrations which are below the range (-2-4 M) where the unfolding transition takes place. Evidence from N M R spectroscopy shows that various identifiable groups on RNase undergo changes in chemical shift a t pretransition concentrations of this salt, as well as at concentrations in the transition region (Benz and Roberts, 1975). For example, the interactions observed by these authors a t 0.5-0.7 M GdmCl correspond to the wrinkle in the curve of Figure 4. The almost constant residual volume difference (-+0.0003 +
+
+
VOLUME CHANGE BY DENSITY 1.005.
a
1000.
-;
995
3 E
c
”
,990
,985 0.0
0.1
0.2
0.3
0.4
0.5
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0.1
0.2
0.3
0.4
0.5
0.6
I
,780
b
.76 0 CI
E L
>E I
.74c
n I+
,721
1
,701
4 F I G U R E 3: (a) Partial specific volume, 81,of water vs. weight fraction, W3O, of guanidinium chloride with respect to water (20 “ C ) :curve 1 , waterguanidinium chloride; curve 2, water-isoionic ribonuclease A-guanidinium chloride. (b) Partial specific volume, 83. of guanidinium chloride vs. weight fraction, W3O, of guanidinium chloride with respect to water (20 “C): curve 1, water-guanidinium chloride; curve 2, water-isoionic ribonuclease Aguanidinium chloride. The curves in both a and b represent the values of 5i calculated from the smoothed curves of Figure 1.
mL/g3) at all concentrations above 4 M, where the unfolding is presumed to be complete, may not reflect any further interactions of this salt with the protein (the slight peak at W3O = 0.65 may result from the insensitivity of this smoothing procedure at the ends of the two curves in Figure 1). The upward curves O f 43 vs. W3O both in the presence and absence of RNase were essentially parallel in this range (>4 M). Hence, the constant difference in the volume increment after adding a given amount of GdmCl to 1 g of water and after adding the same amount to 1 g of water RNase at all W3O > 0.35 may be viewed in terms of the availability of water. If 1 g of the protein effectively removes 0.50 g of water at all W3O > 0.35, the effect is to raise the value of 43 by the constant amount shown in Figure 4, provided that the protein-denaturant interaction is negligible in this range. Thus, the amount of water removed by the protein when Wzo = 0.500 (i.e., gdgl = 0.05263) is 0.50 g1/g2times 0.05263 gdgl, or 0.0263 g of water
+
per g of the total water present. Hence, 0.9727 g of water is available for solvating the GdmCI. The reduced amount of available water would raise the effective concentration at, for example, W3O = 0.4000 to 0.4064. The value of $3 at the latter concentration in the absence of RNase is the same as that found at W3O = 0.4000 in the presence of the RNase. This calculation neglects the effect on 43 by the comparatively small proportion of GdmCl which may be “bound” to the protein (or more precisely, the amount of GdmCl which is not of the bulk-solvent phase). In these calculations, however, we assume that the additional GdmCl above W3O = 0.35 (>4 M) does not contribute to the “bound” amount. [We estimate the ‘‘bound” amount as 0.53g3/g2 (or about 4% of the total GdmCI in the preceding example) by applying the value for the unavailable water, 0.50gl/g2, in combination with the preferential interaction parameter; some values for the latter were determined in this concentration range by the density-equilibrium dialysis BIOCHEMISTRY, VOL. 16, NO. 1 2 , 1977
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the order of 10 mL/mol of GdmCI) attends the transport of GdmCl from water to water RNase at about equimolar concentrations of GdmC1:RNase. This increase in volume is analogous to that observed when hydrocarbons are transported from water to a nonpolar phase, and suggests that GdmCl spontaneously interacts with the protein phase-the particular interaction decreasing with increasing concentrations of GdmCI. Whether other salts exhibit such increases in specific volume in the presence of about equimolar concentrations of protein is not known. Nonetheless, the titration behavior by a density approach with selected solutes, such as coenzymes, allosteric effectors, etc., may be found useful.
+
Acknowledgments We thank Mr. T. E. Dorrier for his careful weighings and for much of the preparatory work. We are also grateful to Professor J . W . Beams for his abiding interest and stimulation.
F I G U R E 4: The difference in the apparent specific vo!ume, A$3 (= -SV/g3), of guanidinium chloride vs. the weight fraction, W3O, of guani-
dinium chloride with respect to water upon transporting the salt from water to water ribonuclease (20 "C). The curve represents the difference in the values of $3 calculated from the smoothed curves of Figure 1 at a common value of W3O.M3 is the molarity of guanidinium chloride in the ribonuclease solutions for comparing this data with those from other kinds of studies.
+
method (Kupke and Beams, 1972; Kupke, 1973). This "bound" amount corresponds to about 76 mol of GdmCl per mol of isoionic RNase in the posttransition region, in approximate agreement with conclusions drawn from other kinds of studies (cited in Benz and Roberts, 1975).] The upward trend in Figure 4 as W3O 0, however, suggests that the presence of RNase increases the values of 43 (and E,) at very low concentrations of GdmCl (which is not evident from the differences in 53 of Figure 3b). This trend was confirmed by the results of a test with very low concentrations of GdmCI. The values of 53O were estimated from the limiting slope as c3 0 a t five different concentrations of RNase (c2 = 0 to 0.048 g/mL). Although true values of 53O may not have been achieved in these cases, it was clear that the partial specific volume of GdmCl increased significantly with RNase concentration as c3 0. Over the range in c2 which was encompassed in this special study, 53O (apparent) increased linearly from 0.692 to 0.719 mL/g3, or d53O/dc2 N +0.56 mL2 g3-I g2-I. In these experiments, the densities were determined in triplicate, or more, on 10 to 40 different concentrations of the 5 series ranging from -0.01 to 0.2% GdmCI. The values of E3O (apparent) were obtained via eq 3 from a linear least-squares fit to the data in each series. The assignment of linearity was arbitrary, but over this short concentration range the substantial differences in the values illustrate sufficiently the increase in 5 3 O with c2. A confirmatory aspect is provided by the observation that the individual values of 43 increased as c3 0 in the four series containing RNase, but decreased a s c3 0 in the series containing no RNase (the latter trend is commonly observed for many salts and other small solutes in water). Indeed, individual values of 43 a t a level of -1 mol of GdmCl per mol of RNase (though subject to greater error in this range) were approximately 0.8 mL/g or even somewhat higher. [An apparent break occurred in plotting 43 vs. W3O at -3 mol of GdmCl per mol of RNase; cf. Benz and Roberts (1975).] Thus, a relatively large positive volume change (on
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Appendix A W e wish to convert the observed density of the protein solution a t each g3/gl in a series, where only component 3 is varied, to a standard density, ~ ( ~ which 1 , reflects a designated value of gdg1 (grams of protein per gram of water) a t any value of g3/gl (or W3O). Thus, different stock solutions may be utilized in preparing a density-composition table over a range in component 3 levels without the chore and additional error of attempting to match each stock solution to some common value of W2O. The densities of curve 2, Figure 1, were converted to the basis of W2°(s)= 0.05 (or g2(s)/g1= 0.0526). The conversion to a standard density assumes that 42 is constant in c2 a t each value of g3/gl, an assumption which should be tested by observing p vs. c2 on new systems. Thus, at constant temperature and pressure, the standard density is given by eq 5, which in linear form is: p(s)
= (1 - 42pO)cp
+ po
(8)
In practice, c2(s)is given by P ( ~ ) W where ~ ( ~ ) W2(s)at each g3/g1 is obtained from the assigned value of W2°(s) by: W20(S)(1
w2(s)=
1
- Wz0(s))-I
+ g3/g1 + W,O(S)(l - w20q-1 -
g2'S)/g1
1
+ g3/gl + g2@)/gl
(9)
Substituting eq 9 into eq 8 and recalling the definition of C Z ( ~ ) gives eq 10. p(s) = PO[
1
- ( 1 - 42pO) W2(s)]-I
(10)
Values of 42 need not be determined a t each g3/gl in order to obtain p ( s ) since eq 5 can be rewritten:
whereby eq 10 becomes:
In this case p and W2 are the experimentally determined values with the actual stock solutions employed; W2(s)is given by eq 9 and po is the value a t g3/glcontaining no protein as obtained via eq 7 and the appropriate coefficients (Table I in our case). In projecting the relationship between the standard density and the weight fraction of component 3 (as in Figure l ) , the
VOLUME CHANGE BY DENSITY
standard weight fraction, W3(s),must be used. The latter is related to the assigned value of W2°(s)by:
W3W =
g3/0
1
+ g3/g1 t W20(S)(l - W,O(s))-'
(13)
Obviously, any number of solutions in any proportion along a regression curve may be used for evaluating the total volume change of mixing if the effect of a perturbant is essentially reversible. In addition, such AV can be evaluated for any concentration of protein if p is a linear function of c2 by generating curves at assigned values of W2°(s)as shown in Appendix A. For mixing a solution from curve 1 with a solution from curve 2 (Figure l ) , no further curves need be generated for AV,i, if (dpldcz),,, is constant at various W3O.
where each g3/gl is the experimental value and is independent of W2°(s)(or g2(s)/gl).I n the case of Figure 1 , curve 2, the standard density was plotted as a function of W3O instead of W3(s)for ease of comparing the data with those from the water-GdmC1 series (curve 2). W3O, being independent of the presence of any component 2, is also given by eq 13 with WZO(~) References preset to zero. Almeida, S. P., and Crouch, T. H. (1 97 l ) , Reu. Sci. Instrum. 42, 1344. Appendix B Beams, J. W., and Clarke, A. M. (1962), Rec. Sci. Instrum. 33, 730. The AV of mixing of any two solutions A and B can be determined from the masses, mA and mB, which are to be mixed Benz, F. W., and Roberts, G. C. K. (1975), J . Mol. Biol. 91, and the densities before and after mixing. The total volume 367. before mixing is the sum of the masses each divided by its Hantgan, R. R., Hammes, G. G., and Scheraga, H. A. (1974), density, i.e., [mA/pAt mB/PB].Determination of the density, Biochemistry 13, 3421. p A B , after mixing yields the final volume, [mAB/PAB],where Hunter, M. J. (1966), J . Phys. Chem. 70, 3285. AB denotes the mixture. The difference in volume is the A V Katz, S., and Ferris, T. G. (1966), Biochemistry 5 , 3246. of mixing given by eq 14. Kauzmann, W. (1959), Adu. Protein Chem. 14, 1 (see pp 15- 16). Kupke, D. W. (1973), in Physical Principles & Techniques in AV,,,=Z(14) Protein Chemistry, Part C, Leach, S. J., Ed., New York, N.Y., Academic Press, p 1. With a regression curve available for a known concentration Kupke, D. W., and Beams, J . W. (1972), Methods Enzymol. of protein, WzO,or a standard concentration, WzO(S),such as 26, 74. in curve 2 of Figure 1 , P A and P B are obtained directly for the Nozaki, Y. (1972), Methods Enzymol. 26, 43. chosen solutions of weight fractions W3,A and W3,B,respecPlato, F. (1900), Kaiserlichen Normal-Eichungs-Kommision, tively, via eq 7 and the appropriate coefficients. The value of Wiss. Abh. 2, 153; quoted in Bates, F. J., et al., Ed. ( 1 942), AB for the mixture is found similarly after calculating W3,AB Natl. Bur. Stand. (US.), Circ. No. 440, pp 626ff. in terms of the designated masses, mA and mB, of solutions of Senter, J. P. (1969), Rec. Sci. Instrum. 40, 334 (adapted from weight fraction W3,Aand W33, respectively. Thus: Beams and Clarke, 1962). Skerjanc, J., Dolecek, V., and Lapanje, S. ( 1 970), Eur. J. Biochem. 17. 160.
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